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In the context of single-base station (BS) non-line-of-sight (NLoS)single-epoch localization with the aid of a reflective reconfigurableintelligent surface (RIS), this paper introduces a novel three-step algorithmthat jointly estimates the position and velocity of a mobile user equipment(UE), while compensating for the Doppler effects observed in near-field (NF) atthe RIS elements over the short transmission duration of a sequence of downlink(DL) pilot symbols. First, a low-complexity initialization procedure isproposed, relying in part on far-field (FF) approximation and a static userassumption. Then, an alternating optimization procedure is designed toiteratively refine the velocity and position estimates, as well as the channelgain. The refinement routines leverage small angle approximations and thelinearization of the RIS response, accounting for both NF and mobility effects.We evaluate the performance of the proposed algorithm through extensivesimulations under diverse operating conditions with regard to signal-to-noiseratio (SNR), UE mobility, uncontrolled multipath and RIS-UE distance. Ourresults reveal remarkable performance improvements over the state-of-the-art(SoTA) mobility-agnostic benchmark algorithm, while indicating convergence ofthe proposed algorithm to respective theoretical bounds on position andvelocity estimation.

RIS-Enabled NLoS Near-Field Joint Position and Velocity Estimation under User Mobility